1. Field of the Invention
Example embodiments relate to optical technology, and more particularly, to an axi-symmetric lens having an extended depth of focus, and an optical system having the axi-symmetric lens.
2. Description of the Related Art
In general, a depth of focus (DOF) is one of the major characteristics of an optical system defining a distance range between an object plane and a lens, or a distance range between a lens and an image plane, to obtain a clear image. The major factors determining the DOF include aperture size and aberration of various optical lenses.
A general optical system using thin lens approximation is inappropriate for use in a variety of industrial fields using laser material processing, lithography, or light projection and image processing. In these industrial fields, a demand for an optical system having a DOF improved to that of a general optical system has increased,
According to “Wave Front Coding” written by Dowksi et al., a solution for an optical system having an extended depth of focus (EDOF) is to insert a phase plate in an aperture stop of an optical system. Because the phase plate has a small divergence in light distribution at a focal point, asymmetrical distortion of a wave front is generated to increase the DOF.
Accordingly, because a point spread function (PSF) of an optical system has asymmetrical and important space dimensions, image post-processing to remove the dimensions is needed. Although the image post-processing may be solved based on the characteristic of a PSF profile that may be perpendicularly separated, the asymmetry of the PSF may reduce allowance of design errors in an EDOF system.
As another method of realizing the EDOF, a plurality of Fresnel lenses having different focal distances are multiplexed as a single optical element. The apertures of the Fresnel lenses are arranged on the entire surface and divided into independent portions. The portions are divided again into a plurality of sub-portions. Appropriate Fresnel lens portions are used to fill the sub-portions.
The uniform distribution of the portions and the sub-portions may generate undesired image duplication. Because the image duplication may be removed by randomizing the portions and sub-portions of the aperture division, a clear image may be obtained without the post-processing of an image. However, the optical system has problems with discontinuity, asymmetry, and randomization that may deteriorate the performance of the EDOF system.
As another method of realizing the EDOF, a lens that is symmetric, divided into a plurality of zones, and has a smooth surface is used as an aspherical lens. The focal distance of the lens continuously varies from a near distance to a far distance while the optical performance is similar in each zone. However, this structure is appropriate for the aspherical lens, but inappropriate for a portion exceeding the optical performance of an eye. An optical system having a improved performance may be obtained by eliminating the defects on the lens surface.